Answer:
1 day: 4480
2 days: 8960
3 days: 13440
[tex]f^{-1}(x) = \sqrt{\frac{x -4}{4}}[/tex] ---- function inverse
Step-by-step explanation:
Given
[tex]f(x) = 70 \cdot 64x[/tex]
Solving (a): The amount present after 1 day.
Here, [tex]x =1[/tex]
So:
[tex]f(1) = 70 \cdot 64*1= 4480[/tex]
Solving (b): The amount present after 2 days.
Here, [tex]x =2[/tex]
So:
[tex]f(2) = 70 \cdot 64*2= 8960[/tex]
Solving (c): The amount present after 3 days.
Here, [tex]x = 3[/tex]
So:
[tex]f(3) = 70 \cdot 64*2= 13440[/tex]
Solving (d): The inverse function of:
[tex]f(x)= 4x^2 + 4[/tex]
Replace f(x) with y
[tex]y= 4x^2 + 4[/tex]
Swap x and y
[tex]x= 4y^2 + 4[/tex]
Rewrite as:
[tex]4y^2 = x -4[/tex]
Divide by 4
[tex]y^2 = \frac{x -4}{4}[/tex]
Take square roots
[tex]y = \sqrt{\frac{x -4}{4}}[/tex]
Replace y with function inverse
[tex]f^{-1}(x) = \sqrt{\frac{x -4}{4}}[/tex]
