TS ICET 2015 Question Paper with Solutions for online practice

Question : 121 of 200

Marks: +1, -0

If f : R → R and g : R → R are defined by f(x) = 2X and g(x) =

x^2

for each x ∊ R, then {x ∊ R : (fog) (x) = (gof) (x)} =

Solution:

Given

f(x)=2^x;g(x)=x^2

∴\fog(x)=f[g(x)]=f(x^2)=2^{x^2}

........(i)

gof(x)=g[f(x)]=g(2^x)=(2^x)^2=2^{2x}

...(ii)

Since, fog(x) = gof(x) [Given]

⇒2^{x^2}=2^{2x}

[from (i) and (ii)]

⇒x^2=2x

⇒x(x–2)=0⇒x=0,2

∴x=\{0,2\}

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