Question

If f(x)=x-1,g(x)=3x+1 and h(x)=x2,show that (f o g)o h=f o(g o h)
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Answer 1

Question :

$f(x) = x - 1 \: g(x) = 3x + 1 \: \: h(x) = {x}^{2}$

$show \: that \: (fog)oh = fo(goh)$

Answer :

● Lets have ( fog )oh in RHS and fo( goh ) in LHS

$fog = f(g(x))$

$= f(3x + 1)$

● Now we need to substitute the value of g (x) in Function of x in f

$f(x) = x - 1$

$f(g(x)) = (3x + 1) - 1$

$= 3x$

● Now lets find the value of ( fog )oh Substitute the value of h(x) in function of (fog)

$fog(h(x))$

$fog( {x}^{2} )$

$3( {x}^{2} )$

$3 {x}^{2}$

_________《 RHS 》

● Now let's find the the value of LHS

● have the value of (goh) in fo(goh)

$goh = g(h(x))$

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

● Now let's substitute the value of h(x) in the function of x in g

= 3 (x^2) + 1

= 3x^2 + 1

● Now let's substitute the value of ( goh ) in function of x in f

= (3x^2 + 1) - 1

= 3x^2 _______LHS

RHS = LHS

Hence showed that (fog)oh = fo(goh).

Be Delighted :)

Answer 2

3x ^2 = 3x ^2

RHS = LHS

HENCE SHOWED