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?
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,
[tex]f(g(x))=x=g(f(x))[/tex]
1) [tex]f(x) = 8x-10,\ g(x) = (x + 10)[/tex]
[tex]f(g(x))=f(x+10)[/tex]
[tex]f(g(x))=8(x+10)-10[/tex]
[tex]f(g(x))=8x+80-10[/tex]
[tex]f(g(x))=8x+70[/tex]
As [tex]f(g(x))\neq x[/tex]
[tex]g(f(x))=g(8x-10)[/tex]
[tex]g(f(x))=8x-10+10[/tex]
[tex]g(f(x))=8x[/tex]
As the condition is not satisfied.
2) [tex]f(x) =4x+5,\ g(x) =4x-5[/tex]
[tex]f(g(x))=f(4x-5)[/tex]
[tex]f(g(x))=4(4x-5)+5[/tex]
[tex]f(g(x))=16x-20+5[/tex]
[tex]f(g(x))=16x-15[/tex]
As [tex]f(g(x))\neq x[/tex]
[tex]g(f(x))=g(4x+5)[/tex]
[tex]g(f(x))=4(4x+5)-5[/tex]
[tex]g(f(x))=16x+20-5[/tex]
[tex]g(f(x))=16x+15[/tex]
As the condition is not satisfied.
Both are not inverse functions.
