Question

Determining weather two dung ions are inverse of each other

Answer 1

a)

Functions given:

$f(x)=\frac{3}{x}$$g(x)=\frac{3}{x}$

Procedure

• f(g(x))

Substituing g(x) in the x present in f(x)

$f(g(x))=\frac{3}{(\frac{3}{x})}$

Simplifying:

$f(g(x))=\frac{3\cdot x}{3}$$f(g(x))=x$

• g(f(x))

Substituing f(x) in the x present in g(x)

$g(f(x))=\frac{3}{(\frac{3}{x})}$

Simplifying

$g(f(x))=\frac{3\cdot x}{3}$$g(f(x))=x$

Since f(g(x)) = g(f(x)) = x, the given equation and the computed inverse are really inverse functions.

b)

$f(x)=2x-7$$g(x)=2x+7$

• f(g(x))

Substituing g(x) in the x present in f(x)

$f(g(x))=2\cdot(2x+7)-7$$f(g(x))=4x+14-7$$f(g(x))=4x+7$

• g(f(x))

Substituing f(x) in the x present in g(x)

$g(f(x))=2\cdot(2x-7)+7$$g(f(x))=4x-14+7$$g(f(x))=4x-7$

Then, these functions are NOT inverse.

Answer:

• a) ,f and g are inverses of each other

,

• b) f and g are not inverses of each other