Question

f(x) = x-3, g(x) = 6x-7, h(x) = 2 (to the power x)a) work our the value of x when f(x) = 0.5b) Fing g inverse (2)c) work out the value of x when h(x) = f(11)

Answer 1

The given functions are

$\begin{gathered} f(x)=x-3 \\ \\ g(x)=6x-7 \\ \\ h(x)=2^x \end{gathered}$

a)

Since f(x) = 0.5

Then equate x - 3 by 0.5

$x-3=0.5$

Add 3 to both sides

$\begin{gathered} x-3+3=0.5+3 \\ x=3.5 \end{gathered}$

The value of x is 3.5

b)

To find the inverse of g do these steps

1. Replace g(x) by y

$y=6x-7$

2. Switch x and y

$x=6y-7$

3. Solve to find y

$\begin{gathered} x+7=6y-7+7 \\ x+7=6y \\ \frac{x+7}{6}=y \\ \\ y=\frac{x+7}{6} \end{gathered}$

4. Replace y by g^(-1)

$g^{-1}(x)=\frac{x+7}{6}$

Substitute x by 2

$g^{-1}(2)=\frac{2+7}{6}=\frac{9}{6}=\frac{3}{2}=1.5$

The value of g inverse of 2 is 1.5

c)

Find at first f(11)

$\begin{gathered} f(11)=11-3 \\ f(11)=8 \end{gathered}$

Equate h(x) by 8

$2^x=8$

Since 8 = 2 x 2 x 2, then

$8=2^3$

Replace 8 by 2^3

$2^x=2^3$

By using the rule of equal bases (their powers are equal), then

$x=3$

The value of x is 3