Math / Algebra

QuestionModule 3.4 $\text { If } f(x)=2 x+1 \text { and } g(x)=3 x-1 \text {, then } f(g(x))=$ $5 x$ $6 x+2$ $6 x^{2}+x-1$ $6 x-1$ $x-2$

Studdy Solution

STEP 1

1. We are given two functions: $f(x) = 2x + 1$ and $g(x) = 3x - 1$ .
2. We need to find the composition of these functions, $f(g(x))$ .
3. We will evaluate $f(g(x))$ and match it with the given options.

STEP 2

1. Substitute $g(x)$ into $f(x)$ .
2. Simplify the expression for $f(g(x))$ .
3. Compare the simplified expression with the given options.

STEP 3

Substitute $g(x) = 3x - 1$ into $f(x) = 2x + 1$ :
$f(g(x)) = f(3x - 1)$

STEP 4

Substitute $3x - 1$ into the function $f(x)$ :
$f(3x - 1) = 2(3x - 1) + 1$

STEP 5

Simplify the expression:
$f(3x - 1) = 2 \cdot 3x - 2 \cdot 1 + 1$ $f(3x - 1) = 6x - 2 + 1$ $f(3x - 1) = 6x - 1$

STEP 6

Compare the simplified expression $6x - 1$ with the given options:
- $5x$ - $6x + 2$ - $6x^2 + x - 1$ - $6x - 1$ - $x - 2$
The expression $6x - 1$ matches the option $6x - 1$ .
The value of $f(g(x))$ is:
$\boxed{6x - 1}$

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QuestionModule 3.4 $\text { If } f(x)=2 x+1 \text { and } g(x)=3 x-1 \text {, then } f(g(x))=$ $5 x$ $6 x+2$ $6 x^{2}+x-1$ $6 x-1$ $x-2$

Studdy Solution

STEP 1

1. We are given two functions: $f(x) = 2x + 1$ and $g(x) = 3x - 1$ .
2. We need to find the composition of these functions, $f(g(x))$ .
3. We will evaluate $f(g(x))$ and match it with the given options.

STEP 2

1. Substitute $g(x)$ into $f(x)$ .
2. Simplify the expression for $f(g(x))$ .
3. Compare the simplified expression with the given options.

STEP 3

Substitute $g(x) = 3x - 1$ into $f(x) = 2x + 1$ :
$f(g(x)) = f(3x - 1)$

STEP 4

Substitute $3x - 1$ into the function $f(x)$ :
$f(3x - 1) = 2(3x - 1) + 1$

STEP 5

Simplify the expression:
$f(3x - 1) = 2 \cdot 3x - 2 \cdot 1 + 1$ $f(3x - 1) = 6x - 2 + 1$ $f(3x - 1) = 6x - 1$

STEP 6

Compare the simplified expression $6x - 1$ with the given options:
- $5x$ - $6x + 2$ - $6x^2 + x - 1$ - $6x - 1$ - $x - 2$
The expression $6x - 1$ matches the option $6x - 1$ .
The value of $f(g(x))$ is:
$\boxed{6x - 1}$

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QuestionModule 3.4 If f(x)=2x+1 and g(x)=3x−1, then f(g(x))=\text { If } f(x)=2 x+1 \text { and } g(x)=3 x-1 \text {, then } f(g(x))= If f(x)=2x+1 and g(x)=3x−1, then f(g(x))= 5x5 x5x 6x+26 x+26x+2 6x2+x−16 x^{2}+x-16x2+x−1 6x−16 x-16x−1 x−2x-2x−2

Studdy Solution

STEP 1

1. We are given two functions: f(x)=2x+1 f(x) = 2x + 1 f(x)=2x+1 and g(x)=3x−1 g(x) = 3x - 1 g(x)=3x−1.2. We need to find the composition of these functions, f(g(x)) f(g(x)) f(g(x)).3. We will evaluate f(g(x)) f(g(x)) f(g(x)) and match it with the given options.

STEP 2

1. Substitute g(x) g(x) g(x) into f(x) f(x) f(x).2. Simplify the expression for f(g(x)) f(g(x)) f(g(x)).3. Compare the simplified expression with the given options.

STEP 3

Substitute g(x)=3x−1 g(x) = 3x - 1 g(x)=3x−1 into f(x)=2x+1 f(x) = 2x + 1 f(x)=2x+1:f(g(x))=f(3x−1) f(g(x)) = f(3x - 1) f(g(x))=f(3x−1)

STEP 4

Substitute 3x−1 3x - 1 3x−1 into the function f(x) f(x) f(x):f(3x−1)=2(3x−1)+1 f(3x - 1) = 2(3x - 1) + 1 f(3x−1)=2(3x−1)+1

STEP 5

Simplify the expression:f(3x−1)=2⋅3x−2⋅1+1 f(3x - 1) = 2 \cdot 3x - 2 \cdot 1 + 1 f(3x−1)=2⋅3x−2⋅1+1 f(3x−1)=6x−2+1 f(3x - 1) = 6x - 2 + 1 f(3x−1)=6x−2+1 f(3x−1)=6x−1 f(3x - 1) = 6x - 1 f(3x−1)=6x−1

STEP 6

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QuestionModule 3.4 $\text { If } f(x)=2 x+1 \text { and } g(x)=3 x-1 \text {, then } f(g(x))=$ $5 x$ $6 x+2$ $6 x^{2}+x-1$ $6 x-1$ $x-2$

1. We are given two functions: $f(x) = 2x + 1$ and $g(x) = 3x - 1$ .
2. We need to find the composition of these functions, $f(g(x))$ .
3. We will evaluate $f(g(x))$ and match it with the given options.

1. Substitute $g(x)$ into $f(x)$ .
2. Simplify the expression for $f(g(x))$ .
3. Compare the simplified expression with the given options.

Substitute $g(x) = 3x - 1$ into $f(x) = 2x + 1$ :
$f(g(x)) = f(3x - 1)$

Substitute $3x - 1$ into the function $f(x)$ :
$f(3x - 1) = 2(3x - 1) + 1$

Simplify the expression:
$f(3x - 1) = 2 \cdot 3x - 2 \cdot 1 + 1$ $f(3x - 1) = 6x - 2 + 1$ $f(3x - 1) = 6x - 1$