Question

If f(x) = 7 + 2x and g(x) = 5x - 2, find fg(7).693703-693-703

Answer 1

SOLUTION:

Step 1 :

In this question, we are meant to find the value of:

$f\text{ g ( 7 )}$$\begin{gathered} \text{If f(x ) = 7 + 2x } \\ \text{and g ( x ) = 5 x - 2} \end{gathered}$

Step 2 :

$\begin{gathered} \text{Given fg ( x ) = f ( g ( x ) ) } \\ \operatorname{Re}call\text{ that f ( x ) = 7 + 2 x } \\ f\text{ ( g( x ) ) = f ( 5 x- 2 )} \\ \text{Then f ( x ) = 7 + 2x } \\ f\text{ ( 5 x- 2 ) = 7 + 2 ( 5 x -2 )} \\ \end{gathered}$$\begin{gathered} f\text{ }(\text{ 5 x - 2 ) = 7 + 10 x - 4} \\ f\text{ ( 5 x- 2 ) = 10 x + 3} \\ f\text{ ( g ( 7 ) )= 10 ( 7 ) + 3} \\ f\text{ ( g ( 7 ) })\text{ = 70 + 3} \\ f\text{ ( g ( 7 ) ) = 73} \end{gathered}$

CONCLUSION:

The value of fg ( 7 ) = 73.