QuestionFind $x$ such that $f(x)=x$ for $f(x)=\frac{3}{4} x+12$ .

Studdy Solution

STEP 1

Assumptions1. The function is defined as $f(x)=\frac{3}{4} x+12$ . We need to find the value of $x$ when $f(x)=x$

STEP 2

To find the value of $x$ when $f(x)=x$ , we need to set $f(x)$ equal to $x$ and solve for $x$ .
$f(x) = x$

STEP 3

Substitute the given function $f(x)=\frac{3}{} x+12$ into the equation.
$\frac{3}{} x+12 = x$

STEP 4

To solve for $x$ , we need to get all terms involving $x$ on one side of the equation. Subtract $\frac{3}{4} x$ from both sides of the equation.
$12 = x - \frac{3}{4} x$

STEP 5

Notice that on the right side of the equation, we have $x$ in terms of itself. To simplify, we can combine these terms by finding a common denominator.
$12 = \frac{4}{4}x - \frac{3}{4} x$

STEP 6

Subtract the fractions on the right side of the equation.
$12 = \frac{1}{4}x$

STEP 7

To isolate $x$ , we can multiply both sides of the equation by the reciprocal of $\frac{1}{4}$ , which is $4$ .
$12 \times4 = x$

STEP 8

Calculate the value of $x$ .
$x =12 \times4 =48$ The value of $x$ when $f(x)=x$ is $48$ .

Was this helpful?

QuestionFind $x$ such that $f(x)=x$ for $f(x)=\frac{3}{4} x+12$ .

Studdy Solution

STEP 1

Assumptions1. The function is defined as $f(x)=\frac{3}{4} x+12$ . We need to find the value of $x$ when $f(x)=x$

STEP 2

To find the value of $x$ when $f(x)=x$ , we need to set $f(x)$ equal to $x$ and solve for $x$ .
$f(x) = x$

STEP 3

Substitute the given function $f(x)=\frac{3}{} x+12$ into the equation.
$\frac{3}{} x+12 = x$

STEP 4

To solve for $x$ , we need to get all terms involving $x$ on one side of the equation. Subtract $\frac{3}{4} x$ from both sides of the equation.
$12 = x - \frac{3}{4} x$

STEP 5

Notice that on the right side of the equation, we have $x$ in terms of itself. To simplify, we can combine these terms by finding a common denominator.
$12 = \frac{4}{4}x - \frac{3}{4} x$

STEP 6

Subtract the fractions on the right side of the equation.
$12 = \frac{1}{4}x$

STEP 7

To isolate $x$ , we can multiply both sides of the equation by the reciprocal of $\frac{1}{4}$ , which is $4$ .
$12 \times4 = x$

STEP 8

Calculate the value of $x$ .
$x =12 \times4 =48$ The value of $x$ when $f(x)=x$ is $48$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind xxx such that f(x)=xf(x)=xf(x)=x for f(x)=34x+12f(x)=\frac{3}{4} x+12f(x)=43​x+12.

Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=34x+12f(x)=\frac{3}{4} x+12f(x)=43​x+12 . We need to find the value of xxx when f(x)=xf(x)=xf(x)=x

STEP 2

To find the value of xxx when f(x)=xf(x)=xf(x)=x, we need to set f(x)f(x)f(x) equal to xxx and solve for xxx.f(x)=xf(x) = xf(x)=x

STEP 3

Substitute the given function f(x)=3x+12f(x)=\frac{3}{} x+12f(x)=3​x+12 into the equation.3x+12=x\frac{3}{} x+12 = x3​x+12=x

STEP 4

To solve for xxx, we need to get all terms involving xxx on one side of the equation. Subtract 34x\frac{3}{4} x43​x from both sides of the equation.12=x−34x12 = x - \frac{3}{4} x12=x−43​x

STEP 5

Notice that on the right side of the equation, we have xxx in terms of itself. To simplify, we can combine these terms by finding a common denominator.12=44x−34x12 = \frac{4}{4}x - \frac{3}{4} x12=44​x−43​x

STEP 6

Subtract the fractions on the right side of the equation.12=14x12 = \frac{1}{4}x12=41​x

STEP 7

To isolate xxx, we can multiply both sides of the equation by the reciprocal of 14\frac{1}{4}41​, which is 444.12×4=x12 \times4 = x12×4=x

STEP 8

Calculate the value of xxx.x=12×4=48x =12 \times4 =48x=12×4=48The value of xxx when f(x)=xf(x)=xf(x)=x is 484848.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind $x$ such that $f(x)=x$ for $f(x)=\frac{3}{4} x+12$ .

Assumptions1. The function is defined as $f(x)=\frac{3}{4} x+12$ . We need to find the value of $x$ when $f(x)=x$

To find the value of $x$ when $f(x)=x$ , we need to set $f(x)$ equal to $x$ and solve for $x$ .
$f(x) = x$

Substitute the given function $f(x)=\frac{3}{} x+12$ into the equation.
$\frac{3}{} x+12 = x$

To solve for $x$ , we need to get all terms involving $x$ on one side of the equation. Subtract $\frac{3}{4} x$ from both sides of the equation.
$12 = x - \frac{3}{4} x$

Notice that on the right side of the equation, we have $x$ in terms of itself. To simplify, we can combine these terms by finding a common denominator.
$12 = \frac{4}{4}x - \frac{3}{4} x$

Subtract the fractions on the right side of the equation.
$12 = \frac{1}{4}x$

To isolate $x$ , we can multiply both sides of the equation by the reciprocal of $\frac{1}{4}$ , which is $4$ .
$12 \times4 = x$

Calculate the value of $x$ .
$x =12 \times4 =48$ The value of $x$ when $f(x)=x$ is $48$ .