If f(x + y) = f(x)f(y) and f(5) = 4, then f(10) – f(-10) is equal to

Question

If f(x + y) = f(x)f(y) and f(5) = 4, then f(10) &ndash; f(-10) is equal to

Accepted Answer

15.9375 — Easy From $f(x+y)=f(x)f(y)$, first find $f(0)$, then build $f(10)$ from $f(5)$, and get $f(-10)$ from the fact that $f(10)f(-10)=f(0)$. 1 Find $f(0)$. Put $y=0$: $f(x)=f(x)\,f(0)$. Since $f(5)=4
eq0$, $f$ is not identically zero, so $f(0)=1$. $$\begin{aligned} &f(x)=f(x)\,f(0)\ &\Rightarrow\ f(0)=1 \end{aligned}$$ 2 Find $f(10)$. Write $10=5+5$. $$\begin{aligned} &f(10)=f(5)\,f(5)=4	imes4\ &\Rightarrow\ f(10)=16 \end{aligned}$$ 3 Find $f(-10)$. Since $f(10)\,f(-10)=f(0)=1$ (from step 1). $$\

CAT 2020 Slot 3 — QA Question 9

Answer & solution