Question

please help and answer in full​

Answer 1

Answer:

f(x) = 2x³ + 3

Here we take y as f(x)

y = 2x³ + 3

if we need inverse thr function,first we must subject ‘x’.

substract both sides by 3

y - 3 = 2x³

divide both sides by 2

(y - 3)/2 = x³

apply square root of three to both sides

[(y - 3)/2]⅓ =(x³)⅓

[(y - 3)/2]⅓ =x

x = [(y - 3)/2]⅓

here f(y)-¹ = x

f(y)-¹ = [(y - 3)/2]⅓

apply x instead of y

f(x)-¹ = [(x - 3)/2]⅓

f(x)-¹ = g(x) = inverse function

g(x) = [(x - 3)/2]⅓  → REQUIRED ANSWER

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