Question

Let $f(x)=-2x^2+1$ and $g(x)=4x-3$, then $(g \circ f)(-1)$ is equal to

• A. 9
• B. $-9$
• C. 7
• D. $-7$
• E. $-8$

Hint:

Function Tip: In composition $g(f(x))$, always solve the inside function first, then substitute into the outside function.

Answer 1

The Correct Option is D

Concept:
The composition of functions $(g \circ f)(x)$ means $g(f(x))$. First apply function $f$, then substitute that result into function $g$.

Step 1: Find $f(-1)$.
Given: $$f(x)=-2x^2+1$$ Substitute $x=-1$: $$f(-1)=-2(-1)^2+1$$

Step 2: Simplify the square term.
Since: $$(-1)^2=1$$ So: $$f(-1)=-2(1)+1=-2+1=-1$$

Step 3: Now apply function $g$.
We need: $$(g \circ f)(-1)=g(f(-1))=g(-1)$$ Given: $$g(x)=4x-3$$

Step 4: Calculate $g(-1)$.
Substitute $x=-1$: $$g(-1)=4(-1)-3=-4-3=-7$$

Step 5: Match with options.
The obtained value is $-7$, which matches option (D).