Math Problem Statement

Evaluate functions and solve for values of x in given mathematical expressions.

Solution

The image contains a series of math problems involving functions. I'll break these into manageable sections, solve them, and explain each step clearly.

Let’s address a few at a time. If you have specific numbers you want prioritized, let me know!


Problem 1:

g(x) = -7x; x = 4 Substitute x=4x = 4 into g(x)g(x): g(x)=7(4)=28g(x) = -7(4) = -28


Problem 2:

f(x) = -2x; x = -6 Substitute x=6x = -6 into f(x)f(x): f(x)=2(6)=12f(x) = -2(-6) = 12


Problem 3:

k(x) = 3x - 11; x = -12 Substitute x=12x = -12 into k(x)k(x): k(x)=3(12)11=3611=47k(x) = 3(-12) - 11 = -36 - 11 = -47


Problem 4:

t(x) = 9x + 10; x = -1 Substitute x=1x = -1 into t(x)t(x): t(x)=9(1)+10=9+10=1t(x) = 9(-1) + 10 = -9 + 10 = 1


Would you like me to continue solving the rest? Let me know!


Related Questions:

  1. How do you identify the domain of a function in problems like these?
  2. How do you verify the substitution step is done correctly in these evaluations?
  3. What happens to functions like g(x)g(x) when x=0x = 0?
  4. What does the slope in k(x)=3x11k(x) = 3x - 11 represent?
  5. Can you always substitute any real number for xx in such functions? Why or why not?

Tip:

Always double-check your substitutions to ensure the correct value of xx is used in each problem!

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Math Problem Analysis

Mathematical Concepts

Function evaluation
Substitution
Linear equations

Formulas

f(x) = ax + b
g(x) = cx
k(x) = dx + e

Theorems

Basic properties of linear functions
Algebraic substitution principle

Suitable Grade Level

Grades 7-10