Question

Find gof and fog, if
(i) f(x) = |x| and g(x) = |5x - 2|
(ii) f(x) = 8x^3 and g(x) = x^(1/3)

Answer 1

$\bold{Answer :}$

(i)

Given that,

f (x) = | x | and g (x) = | 5x - 2 |

Now, gof (x)

= g (f (x))

= g ( |x| )

= | {5 | x |} - 2 |

and fog (x)

= f (g (x))

= f ( | 5x - 2 | )

= | ( | 5x - 2 | ) |

= | 5x - 2 |

(ii)

Given that,

f (x) = 8x³ and g (x) = x^(1/3)

Now, gof (x)

= g (f (x))

= g (8x³)

= (8x³)^(1/3)

= 2x

and fog (x)

= f (g (x))

= f {x^(1/3)}

= 8 {x^(1/3)}³

= 8x

#$\bold{MarkAsBrainliest}$

Answer 2

(i) f(x) = |x| and g(x) = |5x - 2|
then, gof = g(f(x)) = g(|x|)
= |5|x| - 2|
$\textbf{hence, gof = |5|x| - 2|}$

now, fog = f(g(x)) = f(|5x - 2|)
= ||5x - 2|| = |5x - 2|
$\textbf{hence, fog = |5x - 2|}$

(ii) f(x) = 8x³ and g(x) = x⅓
now, gof = g(f(x)) = g(8x³)
= {(8x³)}⅓ = {(2x)³}⅓
= 2x
$\textbf{hence, gof = 2x}$

fog = f(g(x)) = f(x⅓)
= 8(x⅓)³ = 8x
$\textbf{hence, fog=8x}$