Find the inverses of each of the functions below algebraically.
a.f(x)=3y+5x=18
b.h(t)=−4.9(t+3)^2+45.8
how can f(x) include y?
h = -4.9(t+3)^2+45.8
h^-1 = √((45.8-t)/4.9)-3
Idk can you just help me with a
To find the inverse of a function algebraically, we need to switch the roles of x and y in the equation and solve for y. Let's find the inverses of each function step by step:
a. f(x) = 3y + 5x = 18
Step 1: Switch the roles of x and y:
x = 3y + 5x
Step 2: Solve for y:
x - 5x = 3y
-4x = 3y
y = -4x/3
Therefore, the inverse of function f(x) is f^(-1)(x) = -4x/3.
b. h(t) = -4.9(t+3)^2 + 45.8
Step 1: Switch the roles of t and h:
t = -4.9(h+3)^2 + 45.8
Step 2: Solve for h:
t - 45.8 = -4.9(h+3)^2
-4.9(h+3)^2 = t - 45.8
(h+3)^2 = (t - 45.8) / -4.9
Step 3: Take the square root of both sides:
h + 3 = ± √((t - 45.8) / -4.9)
Step 4: Solve for h:
h = -3 ± √((t - 45.8) / -4.9)
Therefore, the inverse of function h(t) is h^(-1)(t) = -3 ± √((t - 45.8) / -4.9).