JEE Mains · Maths · STD 12 - 1. relation and function
For some \(a, b, c \in N\), let \(f(x)=a x-3\) and \(g ( x )= x ^{ b }+ c , x \in R\). If \((\text { fog })^{-1}( x )=\left(\frac{ x -7}{2}\right)^{1 / 3}\) then \((fog) (ac) + (gof) (b)\) is equal to \(..........\)
- A \(2038\)
- B \(2039\)
- C \(2040\)
- D \(2058\)
Answer & Solution
Correct Answer
(B) \(2039\)
Step-by-step Solution
Detailed explanation
Let \(f o g(x)=h(x)\) \(\Rightarrow h ^{-1}( x )=\left(\frac{ x -7}{2}\right)^{\frac{1}{3}}\) \(\Rightarrow h ( x )= fog ( x )=2 x ^3+7\) \(\text { fog }(x)=a\left(x^b+c\right)-3\) \(\Rightarrow a =2, b =3, c =5\) \(\Rightarrow \operatorname{fog}( ac )= fog (10)=2007\)…
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