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Find g ∘ h(x) given g(x) = -2x - 7 and h(x) = 3x - 10.

a) -6x - 17
b) 6x + 17
c) -6x + 17
d) 6x - 17

1 Answer

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Final answer:

To find the composition function g ∘ h(x), substitute h(x) into g(x) and simplify.

With g(x) = -2x - 7 and h(x) = 3x - 10, the result after substitution and simplification is -6x + 13.

The correct answer isn't in the options.

Step-by-step explanation:

To calculate g ∘ h(x), also known as the composition of the functions g and h, you substitute h(x) into the function g(x). Given g(x) = -2x - 7 and h(x) = 3x - 10, first evaluate h(x) and then substitute that result into g(x).

First step: Evaluate h(x), which is 3x - 10.

Second step: Substitute h(x) into g(x): g(h(x)) = g(3x - 10) = -2(3x - 10) - 7.

Third step: Simplify the expression: -2(3x - 10) - 7 = -6x + 20 - 7.

Final step: Combine the constants: -6x + 20 - 7 = -6x + 13.

The correct answer is -6x + 13.

The correct answer isn't in the options.

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