Question

suppose that $f(x)=f(g(x))$ and $g(14)=2,g(14)=5,f(14)=15,$ and $f(2)=13$. find $f(14)$. 20 no correct answer choice is give. 24 140 65

Explanation:

Step1: Apply chain - rule

The chain - rule states that if $F(x)=f(g(x))$, then $F^{\prime}(x)=f^{\prime}(g(x))\cdot g^{\prime}(x)$.

Step2: Substitute $x = 14$

When $x = 14$, we have $F^{\prime}(14)=f^{\prime}(g(14))\cdot g^{\prime}(14)$.

Step3: Use given values

We know that $g(14)=2$ and $g^{\prime}(14)=5$. So $F^{\prime}(14)=f^{\prime}(2)\cdot5$.

Step4: Substitute $f^{\prime}(2)$ value

Since $f^{\prime}(2)=13$, then $F^{\prime}(14)=13\times5 = 65$.

Answer:

E. 65