Answer:
Range of the function f(x) is all real numbers greater that -4, i.e., (-4,∞).
Step-by-step explanation:
The given function is
[tex]f(x)=(\frac{3}{4})^x-4[/tex]
The value of [tex](\frac{3}{4})^x[/tex] is greater than zero for any value of x.
[tex](\frac{3}{4})^x>0[/tex]
Subtract 4 from both the sides.
[tex](\frac{3}{4})^x-4>0-4[/tex]
[tex]f(x)>-4[/tex]
The value of f(x) is greater than -4 for any value of x.
Therefore, the range of the function f(x) is all real numbers greater that -4,i.e., (-4,∞).
