Question

the function g is defined by g(x)=f(x^2-2x+8)​

Answer 1

Answer:

Hey mate here is your answer

g(x) = f ( x^2 -2x +8 )

Inverting f (x):

Inverting f (x):f (x) = 2x – 1

y = 2x – 1

y + 1 = 2x

(y + 1)/2 = x

(x + 1)/2 = y

(x + 1)/2 = f –1(x)

Inverting g(x):

g(x) = (1/2)x + 4

y = (1/2)x + 4

y – 4 = (1/2)x

2(y – 4) = x

2y – 8 = x

2x – 8 = y

2x – 8 = g –1(x)

Finding the composed function: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

Finding the composed function: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved( f o g)(x) = f (g(x)) = f ((1/2)x + 4)

Finding the composed function: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved( f o g)(x) = f (g(x)) = f ((1/2)x + 4) = 2((1/2)x + 4) – 1

= x + 8 – 1

= x + 7

Inverting the composed function:

Inverting the composed function:( f o g)(x) = x + 7

Inverting the composed function:( f o g)(x) = x + 7 y = x + 7

y – 7 = x

x – 7 = y

x – 7 = ( f o g)–1(x)

Now I'll compose the inverses of f(x) and g(x) to find the formula for (g–1 o f –1)(x):

(g–1 o f –1)(x) = g–1( f –1(x))

= g–1( (x + 1)/2 )

= 2( (x + 1)/2 ) – 8

= (x + 1) – 8

= x – 7 = (g–1 o f –1)(x)

Note that the inverse of the composition (( f o g)–1(x)) gives the same result as does the composition of the inverses ((g–1 o f –1)(x)). So I would conclude that

Note that the inverse of the composition (( f o g)–1(x)) gives the same result as does the composition of the inverses ((g–1 o f –1)(x)). So I would conclude that( f o g)–1(x) = (g–1 o f –1)(x).

thanks

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Answer 2

Answer:

x^2-2x-8

x^2-4x+2x-8

x(x-4) +2(x-4)

(x+2) (x-4)

x=-2

x=4