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.