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QuestionEvaluate f(3)f(3) for f(x)=x2f(x)=x^{2}. A. 3 B. 6 C. 9 D. 12 Solve: 3t−2z=43t-2z=4, 4t+z=74t+z=7. A. (2,−1)(2,-1) B. (−1,2)(-1,2) C. (1,3)(1,3) D. (−3,−2)(-3,-2) Find the inverse of f(x)=2f(x)=2. A. f−1(x)=log⁡2xf^{-1}(x)=\log 2 x B. f−1(x)=ln⁡xf^{-1}(x)=\ln x C. f−1(x)=exf^{-1}(x)=e^{x} D. f−1(x)=x2f^{-1}(x)=x^{2} Calculate log⁡28\log_{2} 8. A. 2 B. 3 C. 4 D. 8 What is log⁡525\log_{5} 25? A. 2 B. 4 C. 6 D. 8 Given log⁡3m+log⁡3m4=2\log_{3} m + \log_{3} m 4 = 2, find mm. A. 2 B. 4 C. 5 D. 6

Studdy Solution

STEP 1

Assumptions1. For problem6, we are given the function f(x)=xf(x) = x^{} and we need to evaluate f(3)f(3). . For problem7, we are given a system of two equations and we need to solve for the variables tt and zz.
3. For problem8, we are given the function f(x)=f(x) = and we need to find its inverse function.
4. For problem9, we are given the logarithm log⁡8\log_{}8 and we need to evaluate it.
5. For problem10, we are given the logarithm log⁡525\log_{5}25 and we need to evaluate it.
6. For problem11, we are given the equation log⁡3m+log⁡3m4=\log_{3}m + \log_{3}m4 = and we need to solve for the variable mm.

STEP 2

For problem6, plug in the value x=x = into the function f(x)f(x).
f()=()2f() = ()^{2}

STEP 3

Calculate the value of f(3)f(3).
f(3)=(3)2=9f(3) = (3)^{2} =9The answer for problem6 is C.9.

STEP 4

For problem7, we can solve the system of equations by substitution or elimination. Let's use substitution. First, solve the second equation for zz.
z=7−4tz =7 -4t

STEP 5

Substitute z=7−4tz =7 -4t into the first equation.
3t−2(7−4t)=43t -2(7 -4t) =4

STEP 6

implify the equation and solve for tt.
3t−14+8t=43t -14 +8t =411t=1811t =18t=1811t = \frac{18}{11}

STEP 7

Substitute t=1811t = \frac{18}{11} into the equation z=7−4tz =7 -4t to solve for zz.
z=7−4(1811)z =7 -4 \left(\frac{18}{11}\right)

STEP 8

Calculate the value of zz.
z=7−7211=−511z =7 - \frac{72}{11} = -\frac{5}{11}The answer for problem7 is not listed in the options. Please check the problem again.

STEP 9

For problem8, the function f(x)=2f(x) =2 is a constant function, not an exponential function. Its inverse does not exist because it's not a one-to-one function. Therefore, none of the options A, B, C, or D is correct.

STEP 10

For problem9, use the definition of logarithm. log⁡28\log_{2}8 is the exponent to which we need to raise2 to get8.
2?=82^{?} =8

STEP 11

Calculate the value of the exponent.
3=8^{3} =8The answer for problem9 is B.3.

STEP 12

For problem10, use the definition of logarithm. log⁡525\log_{5}25 is the exponent to which we need to raise5 to get25.
5?=255^{?} =25

STEP 13

Calculate the value of the exponent.
52=255^{2} =25The answer for problem10 is A.2.

STEP 14

For problem11, use the property of logarithms that the sum of the logarithms of two numbers is equal to the logarithm of their product. So, log⁡3m+log⁡3m4=log⁡3(m×m4)\log_{3}m + \log_{3}m4 = \log_{3}(m \times m4).
log⁡3(m×m4)=2\log_{3}(m \times m4) =2

STEP 15

Use the definition of logarithm to write the equation in exponential form.
32=m×m43^{2} = m \times m4

STEP 16

implify the equation and solve for mm.
9=4m29 =4m^{2}m2=94m^{2} = \frac{9}{4}m=32m = \frac{3}{2}The answer for problem11 is not listed in the options. Please check the problem again.

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