Respuesta :
Answer:
The correct option is 4.
Step-by-step explanation:
Find the x-intercept of each function.
1. [tex]f(x)=5^{(x-5)}-1[/tex]
Substitute f(x)=0, to find the x-intercept.
[tex]0=5^{(x-5)}-1[/tex]
[tex]1=5^{(x-5)}[/tex]
[tex]5^0=5^{(x-5)}[/tex]
On comparing the powers, we get
[tex]0=x-5[/tex]
[tex]x=5[/tex]
The x-intercept of this function is 5.
2. [tex]f(x)=5^{(x-5)}-5[/tex]
Substitute f(x)=0, to find the x-intercept.
[tex]0=5^{(x-5)}-5[/tex]
[tex]5=5^{(x-5)}[/tex]
[tex]5^1=5^{(x-5)}[/tex]
On comparing the powers, we get
[tex]1=x-5[/tex]
[tex]x=6[/tex]
The x-intercept of this function is 6.
3. [tex]f(x)=-5^{(x-5)}+5[/tex]
Substitute f(x)=0, to find the x-intercept.
[tex]0=-5^{(x-5)}+5[/tex]
[tex]5^{(x-5)}=5[/tex]
[tex]5^{(x-5)}=5^1[/tex]
On comparing the powers, we get
[tex]x-5=1[/tex]
[tex]x=6[/tex]
The x-intercept of this function is 6.
4. [tex]f(x)=-5^{(x-5)}-1[/tex]
Substitute f(x)=0, to find the x-intercept.
[tex]0=-5^{(x-5)}-1[/tex]
[tex]1=-5^{(x-5)}[/tex]
[tex]-1=5^{(x-5)}[/tex]
This statement is not true for any value of x. Therefore this function has not x-intercept.
Option 4 is correct.
