Question

$f\left(x\right)=10x-5$. If ${\left(f\left(\frac{b}{4}\right)\right)}^2=25$, find the value of $b$.

• A. $5$
• B. $7$
• C. $14$
• D. $4$

Answer 1

The correct option is D $4$

$f\left(x\right)=10x-5=5(2x-1)$

Now $f\left(\frac{b}{4}\right)=5(\frac{2b}{4}-1)=5(\frac{b}{2}-1)$

Now $f{\left(\frac{b}{4}\right)}^2=25$

$\Rightarrow [5(\frac{b}{2}-1){]}^2=25$

$\Rightarrow 25{(\frac{b}{2}-1)}^2=25$

$\Rightarrow \frac{b}{2}-1=\pm 1$

Hence, $\frac{b}{2}=0$ or $\frac{b}{2}=2$

Therefore $b=0,4$