Question

If $f\left(x\right)=x^2+1$ and $g\left(x\right)=x^2-1$, then what is the value of f[g{h(x)}]?

Given, $h\left(x\right)=\frac{1}{55}\sum _{x=1}^5\left[f\right(x)+g(x\left)\right]$

• A. 45
• B. 32
• C. 70
• D. 10

Answer 1

The correct option is D

10

$h\left(x\right)=\frac{1}{55}\sum _1^5\left[f\right(x)+g(x\left)\right]$

$h\left(x\right)=\frac{1}{55}\sum _1^5\left[\right(x^2+1)+(x^2-1\left)\right]$

$h\left(x\right)=\frac{1}{55}\sum _1^5\left(2x^2\right)$

$\therefore h\left(x\right)=\frac{1}{55}\times 2\times (1^2+2^2+.....+5^2)$

$\therefore h\left(x\right)=\frac{1}{55}\times 2\times \frac{5\times 6\times 11}{6}=2$

$\therefore f\left[g\right\{h\left(x\right)\left\}\right]=f\left[g\right\{2\left\}\right]$
$=f[2^2-1]=f\left[3\right]=3^2+1=10$