Question

I need help with this question

Answer 1

Answer: given and explained briefly below.

In these questions, we go right to left of the function to solve.

(a)

given that

f(x) = x - 3

g(x) = x + 3

(i) fg(x)

= f(x + 3)

= ( x +3 ) -3

= x

(ii) gf(x)

= g(x-3)

= (x-3)+3

= x

to find inverse, we have to make x the subject,

1)

f(x) = x - 3

f(x) + 3 =x

f^-1(x) = x + 3

2)

g(x) = x + 3

g(x) -3 = x

g^-1(x) = x -3

• f and g are inverses of each other

(b)

given that

f(x) = -1/4x

g(x) = 1/4x

fg(x) =

f(1/4x)

1/4(-1/4x)

= x

2)

gf(x)

g(-1/4x)

-1/4(1/4x)

= -x

to find inverse, we have to make x the subject,

1)

f(x) = -1/4x

-1/f(x) = 4x

f^-1(x) = -1/4x

2)

g(x) = 1/4x

x = 1/4g(x)

g^-1(x) = 1/4x

• f and g are not inverses of each other here.