Question

Find the value of $(g\circ f)\left(6\right)$ if $g\left(x\right)=x^2+\frac{5}{2}$ and $f\left(x\right)=\frac{x}{4}-1$.

• A. 2.75
• B. 3
• C. 3.5
• D. 8.625

Answer 1

The correct option is A 2.75

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

$\therefore f\left(6\right)=\frac{6}{4}-1=\frac{3}{2}-1=\frac{1}{2}$

$\therefore \left(gof\right)\left(6\right)=g\left(\frac{1}{2}\right)={\left(\frac{1}{2}\right)}^2+\frac{5}{2}=\frac{11}{4}=2.75$