Question

1. If f (x) = e^x and g(x) = loge x, then show that fog = gof and find f^-1 and g^-1.

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Answer 1

Answer:

1. If f (x) = e^x and g(x) = loge x, then show that fog = gof and find f^-1 and g^-1.

Answer 2

Answer:

f(x)=e

x

;g(x)=lnx

f∘g(x)=e

lnx

=x;g∘f(x)=ln(e

x

)=x

Hence, f∘g(x)=g∘f(x) proved

Let f(x)=y;g(x)=y

e

x

=y;y=lnx

x=lny;x=e

y

∴f

−1

(x)=lnx;f

−1

(x)=e

x