if $f(x)=4 - x^{2}$ and $g(x)=6x$, which expression is equivalent to $(g - f)(3)$?\n$6 - 3-(4 + 3)^{2}$\n$6…

if $f(x)=4 - x^{2}$ and $g(x)=6x$, which expression is equivalent to $(g - f)(3)$?\n$6 - 3-(4 + 3)^{2}$\n$6 - 3-(4 - 3^{2})$\n$6(3)-4 + 3^{2}$\n$6(3)-4 - 3^{2}$

if $f(x)=4 - x^{2}$ and $g(x)=6x$, which expression is equivalent to $(g - f)(3)$?\n$6 - 3-(4 + 3)^{2}$\n$6 - 3-(4 - 3^{2})$\n$6(3)-4 + 3^{2}$\n$6(3)-4 - 3^{2}$

Answer

Explanation:

Step1: Recall the definition of function - subtraction

$(g - f)(x)=g(x)-f(x)$.

Step2: Substitute $x = 3$

$(g - f)(3)=g(3)-f(3)$.

Step3: Find $g(3)$

Given $g(x)=6x$, when $x = 3$, $g(3)=6\times3$.

Step4: Find $f(3)$

Given $f(x)=4 - x^{2}$, when $x = 3$, $f(3)=4-3^{2}$.

Step5: Calculate $(g - f)(3)$

$(g - f)(3)=g(3)-f(3)=6\times3-(4 - 3^{2})=6(3)-4 + 3^{2}$.

Answer:

C. $6(3)-4 + 3^{2}$