Find gof and fog , if, i. f (x) = |x| and g (x) = |5x - 2|
ii. f (x) = 8x³ and g (x) = x^1/3

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A, to a single element 'b' of another non-empty set B.

According to the given problem,

(i).

f (x) = |x| and

g (x) = |5x - 2|

Therefore,

gof (x) = g (f (x))

= g (|x|) = |5 x - 2|

fog (x) = f (g (x))

= f (|5x - 2|) = ||5x - 2||

= |5x - 2|

(ii). f (x) = 8x³ and g (x) = x^1/3

Therefore,

gof (x) = g (f (x))

,= g (8x³) = (8x³)^1/3 = 2x

fog (x) = f (g (x))

= f (x^1/3)³ = 8 (x^1/3)³ = 8x

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.3 Question 3

Find gof and fog , if (i). f (x) = |x| and g (x) = |5x - 2| (ii). f (x) = 8x³ and g (x) = x^1/3

Summary:

For the given function i. f (x) = |x| and g (x) = |5x - 2|, gof (x) = |5x - 2| and ii. f (x) = 8x³ and g (x) = x^1/3 , fog (x) = 8x