Answer:
Option D is correct.
Step-by-step explanation:
Given functions are :
[tex]f(x)=5x-2[/tex]
[tex]g(x)=2^{x} +1[/tex]
Lets see how they change when x changes.
When x = 2
[tex]f(2)=5(2)-2[/tex]
[tex]f(2)=10-2[/tex]
[tex]f(2)=8[/tex]
[tex]g(2)=2^{2} +1[/tex]
[tex]g(2)=4 +1[/tex]
[tex]g(2)=5[/tex]
When x = 4
[tex]f(4)=5(4)-2[/tex]
[tex]f(4)=20-2[/tex]
[tex]f(4)=18[/tex]
[tex]g(4)=2^{4} +1[/tex]
[tex]g(4)=16 +1[/tex]
[tex]g(4)=17[/tex]
When x = 6
[tex]f(6)=5(6)-2[/tex]
[tex]f(6)=30-2[/tex]
[tex]f(6)=28[/tex]
[tex]g(6)=2^{6} +1[/tex]
[tex]g(6)=64 +1[/tex]
[tex]g(6)=65[/tex]
When x = 8
[tex]f(8)=5(8)-2[/tex]
[tex]f(8)=40-2[/tex]
[tex]f(8)=38[/tex]
[tex]g(8)=2^{8} +1[/tex]
[tex]g(8)=256 +1[/tex]
[tex]g(8)=257[/tex]
We can see that as the value of 'x' increases, the value of g(x) will exceed the value of f(x)
So, option D is correct.
Other options are not correct.
