What the inverse of f(x)=4x²

1 answer:

6 0

$f(x)=4x^2\to y=4x^2\\\\\text{Interchange the y and the x}\\\\x=4y^2\\\\\text{Solve for y}\\\\4y^2=x\qquad|:4\\\\y^2=\dfrac{x}{4}\to y=\sqrt{\dfrac{x}{4}}\\\\y=\dfrac{\sqrt{x}}{\sqrt4}\\\\y=\dfrac{\sqrt{x}}{2}\\\\Answer:\ \boxed{f^{-1}(x)=\dfrac{\sqrt{x}}{2}}\ for\ x\geq0$

You might be interested in

Jan bought 6 cookies and 4 doughnuts for 3.50. Tom bought 12 cookies and 5 doughnuts got 5.23. Write and solve a system of equat

iren2701 [21]

0.19 for one cookie and 0.59 for one doughnut

x for how much one cookie costs and y for how much one doughnut costs
6x+4y=3.5
12x+5y=5.23

solve by substitution: (elimination would work too)
4y=3.5-6x
y=0.875-1.5x
12x+5(0.875-1.5x)=5.23
12x+4.375x-7.5x=5.23
4.5x=0.855
x=0.19
now use x to solve for y:
6(0.19)+4y=3.5
1.14+4y=3.5
2.36=4y
y=0.59

Check the work: 6(0.19)+4(0.59)=3.5

4 0

3 years ago

City A grows by 5% every year. In 2021, it has a population of 145,201. What will the population be in 2037?

Diano4ka-milaya [45]

Answer:

About 316,955 people

Step-by-step explanation:

The population of this city can be modeled with the formula $P=I\cdot(1.05^t)$ , where P represents the current population, I represents the initial population, and t represents the amount of time in years since the start of the model. Plugging in 145,201 for I and (2037-2021)=16 for t, we get: