Verify-wether-f-is-invertible-f-x-1-2x-3-

Question Number 165376 by MikeH last updated on 31/Jan/22

Verify wether f is invertible

f (x) = {(1 + 2 x)}^{3}

Answered by Rasheed.Sindhi last updated on 31/Jan/22

f (x) = {(1 + 2 x)}^{3}

y = {(1 + 2 x)}^{3}

1 + 2 x = \sqrt[3]{y}

x = \frac{\sqrt[3]{y} - 1}{2}

f^{- 1} (x) = \frac{\sqrt[3]{x} - 1}{2}

Commented by aleks041103 last updated on 01/Feb/22

I f x \in R, g (x) = x^{3} i s b i j e c t i v e .

F o r a l l x, l (x) = 1 + 2 x i s b i j e c t i v e .

T h e r e f o r e f = g \circ l i s a c o m p o s i t i o n

o f 2 b i j e c t i v e f u n c t i o n s \Rightarrow f i s b i j e c t i v e .

\Rightarrow f i s i n v e r t i b l e, b u t o n l y o n R .