If f(x) = x2 – 1, g(x) = 2x + 1, find fog and gof and domain of fog.

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Solution

Given

f(x) = x2 – 1 and g(x) = 2x + 1

fog(x) = ? and gof(x) = ? and domain of fog = ?

Now,

fog(x) = f(g(x)) = f(2x+1) = (2x + 1)2 – 1

= 4x2 + 4x + 1 – 1

= 4x2 + 4x

 

g0f(x) = g(f(x)) = f(x2 – 1)

= 2(x2 – 1) + 1

= 2x2 – 2 + 1

= 2x2 – 1

 

For Domain of fog(x),

Since 4x2 + 4x is a polynomial equation. So, domain is the set of all real number i.e. domain is (-∞, ∞).

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