Question

If $f\left(x\right)=4x-5,g\left(x\right)=x^2$ and $h\left(x\right)=\frac{1}{x},$ then $f\left(g\right(h\left(x\right)\left)\right)$ is

• A. $\frac{4}{(x-5)}$
• B. $\frac{1}{(4x-5{)}^2}$
• C. $(\frac{x}{4}-5)$
• D. $(\frac{4}{x^2}-5)$

Answer 1

The correct option is D $(\frac{4}{x^2}-5)$

$f\left(x\right)=4x-5;g\left(x\right)=x^2;h\left(x\right)=\frac{1}{x}$

$g\left(h\right(x\left)\right)=\left\{h\right(x){\}}^2={\left(\frac{1}{x}\right)}^2=\frac{1}{x^2}$

$f\left(g\right(h\left(x\right)\left)\right)=4\left(g\right(h\left(x\right)\left)\right)-5$

$=4\left(\frac{1}{x^2}\right)-5=\frac{4}{x^2}-5$

$\therefore$ Answer: option (D)