The function defined by has an inverse on

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

The function g:R→Rg:\mathbb R\to\mathbb R defined by g(x)=x3+4xg(x)=x^{3}+4x has an inverse on R\mathbb R. Which option correctly justifies this fact? (a) gg is surjective onto R\mathbb R, therefore it is invertible. (b) Since g′(x)g'(x) exists for every real xx, gg possesses an inverse function. (c) gg is strictly increasing on R\mathbb R, hence one–one and invertible. (d) Because g(0)=0g(0)=0 and g′(0)≠0g'(0)\neq 0, the inverse–function theorem guarantees that gg is invertible on R\mathbb R.

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