Question

Consider the functions $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=7x+b$. Find the value of $b$, if the composite function, $y=f\left(g\left(x\right)\right)$ passes through $(4,6)$.

• A. $8$
• B. $-8$
• C. $-25$
• D. $-26$
• E. $4-7\sqrt{6}$

Answer 1

The correct option is A $8$

Given, $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=7x+b$

Therefore, $f\left(g\right(x\left)\right)=\sqrt{7x+b}$

Now it passes through $(4,6)$.

Hence, $y_{4,6}={\sqrt{7x+b}}_{4,6}$

$\Rightarrow 6=\sqrt{28+b}$

$\Rightarrow 36=28+b$

$\Rightarrow b=8$