Question

A function g defined for all real x > 0 satisfies g(1) = 1, for all x > 0, then g(4) equals

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$g^{\prime }\left(x^2\right)=x^3\Rightarrow g^{\prime }\left(t\right)=t^2,where{x}^2=t\Rightarrow g\left(t\right)=\frac{t^{\frac{5}{2}}}{\frac{5}{2}}+c\therefore g\left(1\right)=\frac{\left(1\right)\frac{5}{2}}{5/2}+c\therefore c=\frac{3}{5}\therefore g\left(t\right)=\frac{t\frac{5}{2}}{\frac{5}{2}}+\frac{3}{5}g\left(4\right)=\frac{(4{)}^{\frac{5}{2}}}{\frac{5}{2}}+\frac{3}{5}=\frac{67}{5}$