1 Answer

Navyseal · Answer 1 · 2023-12-19T17:22:32+0000

Given the functions:

f(x)=1/4x+5

g(x)=4x-20

The functions g and f are said to commute with each other if g ∘ f = f ∘ g.

Let's check the functions if they are commutative.

a.) f ∘ g = f(g(x))

$f\mleft(x\mright)=(1)/(4)x+5$
f(g(x))=(1)/(4)(4x-20)+5

$f\circ g\text{ = x}$

b.) g ∘ f = g(f(x))

$g\mleft(x\mright)=4x-20$
$g\mleft(f(x)\mright)=4((1)/(4)x+5)-20$
=(4)/(4)x+5(4)-20

$g\circ f\text{ = x}$

Conclusion:

g ∘ f = f ∘ g

Therefore, the functions are commutative.

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