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HELP WITH ALL
Determine the composite functions of the following set of functions

HELP WITH ALL Determine the composite functions of the following set of functions-example-1
User Wrikken
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QUESTION 1

i) Given
f(x)=5x-2 and
g(x)=x^2.


(f\circ g)=f(g(x))


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

We plug in
x^2 into
f(x)=5x-2


(f\circ g)=5x^2-2

ii) Given
f(x)=5x-2 and
g(x)=x^2.


(g\circ f)=g(f(x))


(g\circ f)=g(5x-2)

We plug in
5x-2 into
g(x)=x^2


(g\circ f)=(5x-2)^2


(g\circ f)=25x^2-10x-10x+4


(g\circ f)=25x^2-20x+4

QUESTION 2

i) Given
g(x)=x^2-4 and
h(x)=√(2x+1).


(h\circ g)=h(g(x))


(h\circ g)=h(x^2-4)

We plug in
x^2-4 into
h(x)=√(2x+1)


(h\circ g)=√(2(x^2-4)+1)


(h\circ g)=√(2x^2-8+1)


(h\circ g)=√(2x^2-7)

ii) Given
g(x)=x^2-4 and
h(x)=√(2x+1).


(g\circ h)=g(h(x))


(g\circ h)=g(√(2x+1))

We plug in
\sqrt{2x+1 into
g(x)=x^2-4


(g\circ h)=(√(2x+1))^2-4


(g\circ h)=2x+1-4


(g\circ h)=2x-3

QUESTION 3

i) Given
g(x)=x+5 and
h(x)=√(x-4).


(g\circ h)=g(h(x))


(g\circ h)=g(√(x-4))

We plug in
√(x-4) into
g(x)=x+5


(g\circ h)=√((x-4)+5)

ii) Given
g(x)=x+5 and
h(x)=√(x-4).


(g\circ g)=g(g(x))


(g\circ g)=g(x+5)

We plug in
x+5 into
g(x)=x+5


(g\circ g)=(x+5)+5}


(g\circ g)=x+10}

QUESTION 4

The given functions are;


f(x)=-2x+1 and
g(x)=-x^2


f\circ f=f(f(x))


f\circ f=f(-2x+1)


f\circ f=-2(-2x+1)+1)


f\circ f=4x-2+1)


f\circ f=4x-1)

ii)


g\circ g=g(g(x))


g\circ g=g(-x^2)


g\circ g=-(x^2)^2


g\circ g=-x^4

QUESTION 5


f(x)=5x-2;g(x)=x^2;h(x)=-3x


h\circ g\circ f=h\circ (g(f(x))


h\circ g\circ f=h\circ (g(5x-2))


h\circ g\circ f=h\circ ((5x-2)^2)


h\circ g\circ f=h\circ (25x^2-20x+4)


h\circ g\circ f=h(25x^2-20x+4)


h\circ g\circ f=-3(25x^2-20x+4)


h\circ g\circ f=-75x^2+60x-12)

ii.


f\circ f\circ g=f\circ (f(g(x))


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


f\circ f\circ g=f\circ (5x^2-2)


f\circ f\circ g=f(5x^2-2)


f\circ f\circ g=5(5x^2-2)-2


f\circ f\circ g=25x^2-10-2


f\circ f\circ g=25x^2-12

User Ekky
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