Question

if f(x)=√x and g(x)=x^2 be two functions then find f/g(x) ​

Answer 1

Answer:

f(x)=

1−x

For domain, 1−x≥0

⇒ x≤1

⇒ Domain of f=(−∞,1]

⇒ f:(∞,1]→(0,∞)

g(x)=log

e

x

Clearly, the range of g is not a subset of the domain of f.

So, we need to compute the domain of f∘g.

⇒ Domain (f∘g)=(0,e)→R

⇒ (f∘g)(x)=f[g(x)]

=f(log

e

x)

=

1−log

e

x

The range of f is a subset of the domain of g.

⇒ g∘f:(−∞,1]→R

⇒ (g∘f)(x)=g[f(x)]

=g(

1−x

)

=log

e

(1−x)

2

1

=

2

1

log

e

(1−x)