MHT CET · Maths · Functions
If \(\mathrm{f}(x)=3 \mathrm{x}+10, \mathrm{~g}(x)=x^2-1\), then \((\mathrm{fog})^{-1}(x)=\)
- A \(\left(\frac{x-7}{3}\right)\)
- B \(\left(\frac{x-7}{3}\right)^{\frac{1}{2}}\)
- C \(\left(\frac{x-7}{3}\right)^{\frac{1}{3}}\)
- D \(\left(\frac{3}{x-7}\right)^{\frac{3}{2}}\)
Answer & Solution
Correct Answer
(B) \(\left(\frac{x-7}{3}\right)^{\frac{1}{2}}\)
Step-by-step Solution
Detailed explanation
\(f(g(x)) = 3(x^2-1)+10 = 3x^2+7\) Let \(y = 3x^2+7\). For inverse, \(x = 3y^2+7\)
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