Let be given by

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

g:\mathbb R\to\mathbb R

be given by

g(x)=\dfrac{2x+5}{3}

, and let

h

denote the inverse of

g

. (i) Prove that

h\bigl(g(x)\bigr)=x

for every real

x

. (ii) Simplify the expression

g\bigl(h\bigl(g\bigl(h(x)\bigr)\bigr)\bigr)

, showing each algebraic step clearly. (iii) Hence find the numerical value of

g\bigl(h\bigl(g\bigl(h(11)\bigr)\bigr)\bigr)

.

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