Question

if f(x)= e^x
g(x) =log x, the what is the value of {f of g(x) ​

Answer 1

Answer:

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Step-by-step explanation:

$</p><p>f(x)=ex,g(x)=logxf(x)=ex,g(x)=logx$

$=logf(x) (By defn of g(x))$

$</p><p>=log(ex) (∵f(x)=ex)$

$=x (∵loge=1)$

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