Question

Determine whether each pair of functions are inverse functions. 1) f(x) = 8x – 10, g(x) = (x + 10) 2) f(x) = 4x + 5, g(x) = 4x – 5

Answer 1

Answer:

Both are not inverse functions.

Step-by-step explanation:

To find : Determine whether each pair of functions are inverse functions ?

Solution :

To determine the functions has to satisfy the condition,

$f(g(x))=x=g(f(x))$

1) $f(x) = 8x-10,\ g(x) = (x + 10)$

$f(g(x))=f(x+10)$

$f(g(x))=8(x+10)-10$

$f(g(x))=8x+80-10$

$f(g(x))=8x+70$

As $f(g(x))\neq x$

$g(f(x))=g(8x-10)$

$g(f(x))=8x-10+10$

$g(f(x))=8x$

As the condition is not satisfied.

2) $f(x) =4x+5,\ g(x) =4x-5$

$f(g(x))=f(4x-5)$

$f(g(x))=4(4x-5)+5$

$f(g(x))=16x-20+5$

$f(g(x))=16x-15$

As $f(g(x))\neq x$

$g(f(x))=g(4x+5)$

$g(f(x))=4(4x+5)-5$

$g(f(x))=16x+20-5$

$g(f(x))=16x+15$

As the condition is not satisfied.

Both are not inverse functions.

Answer 2

Answer:

Step-by-step explanation:

To find the inverse of a function you take it in y=f(x) form, switch x and y and then solve for the new y.

So I'll do the first one.

f(x) = 8x-10

y=8x-10 Now switch x and y

x = 8y-10 Now solve for y.  

x+10=8y

(x+10)/8 = y

g(x) is not that, so it is not the inverse.  Can you figure out the second one?