Let the function $f_1$ g and h defined as follows:

f 8 R $\rightarrow$ R, $f(x) = 2_x + 3$

g : R $\rightarrow$ R , g(n) = 3x + 4

h : R $\rightarrow$ R , h(x) = 4x

Find got, fog, foh, gofoh.

Solution:

Let,

f 8 R $\rightarrow$ R, defined as $f(x) = 2_x + 3$

g : R $\rightarrow$ R ,defined as g(n) = 3x + 4

h : R $\rightarrow$ R ,defined as h(x) = 4x

1] gof(x) = g {f(x)}

= g { 2x + 3}

= 3(2x + 3) + 4

= 6x + 9 + 4

= 6x + 13

2] fog = f { g(x)}

= f{3x + 4}

= 2(3x + 4 ) + 3

= 6x + 8 + 3

= 6x + 11

3] foh = f {h(x)}

= f {4x}

= 2(4x) + 3

= 8x + 3

4] gofoh = got { h (x)}

= got {4x}

= g {2(4x) + 3}

= 3[8x + 3] + 4

= 24x + 9 + 4

= 24x + 13