Question

please answer this question.....suppose, f(x)= x^x and g(x)= x^2x. then composite function is?....don't dare to spam.......​

Answer 1

Answer:

f(x) = x^x

g(x) = x^2x

composite function --> f(g(x))

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

= x ^(2x•x)

f(g(x)) = x^(2x²)

Answer 2

Concept:

Composite function: A function whose value is found from two given functions. The first function is applied to an independent variable and then the second function is applied to the result of the first function. This is called a composite function.

Given:

Given functions are,

f(x) = $x^x$

g(x) = $x^{2x}$

Find:

Composite function.

fog and gof or f(g(x)) and g(f(x))

Solution:

Finding fog,

fog = f(g(x))

From (ii), we have g(x) =  $x^{2x}$

∴ f(g(x)) = f( $x^{2x}$)

             = $(x^{2x})^{x^{2x}}$

             = $x^{2x\times x^{2x}}$

             = $x^{2x^{(1+2x)}}$

Now, finding gof,

gof = g(f(x))

But from (i), we have f(x) =  $x^x$

∴ g(f(x)) = g( $x^x$)

            = $(x^x)^{2x^x}$

            = $x^{(x\times 2x^x)}$

            = $x^{2x^{(1+x)}$

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