Determine whether the function is one-to-one. If it is, find itd inverse.
f(x)= 3x+4 over 5
For every x there is an f(x).
For every f(x) (which I'll call y) ther is an x.
y = (3x +4)/5
5y = 3x + 4
x = (5y -4)/3
The inverse function is
f^(-1)(x) = (5x-4)/3
Use the functions f(x)=1/8x-3 and
g(x)=x^3 to find the indicated value or function.
(g^-1 X f^-1)(-3)
Please post this separately.
Looks like you already did. It is answered eleswhere
To determine whether a function is one-to-one, we need to check if each input value (x) corresponds to a unique output value (f(x)).
Let's first find the inverse of the function:
1. Replace f(x) with y:
y = (3x + 4) / 5
2. Interchange x and y:
x = (3y + 4) / 5
3. Solve for y:
Multiply both sides of the equation by 5:
5x = 3y + 4
Subtract 4 from both sides of the equation:
5x - 4 = 3y
Divide both sides of the equation by 3:
(5x - 4) / 3 = y
Therefore, the inverse of the function is:
f^(-1)(x) = (5x - 4) / 3
Now, let's check if the function is one-to-one:
If a function is one-to-one, it means that different input values produce different output values. To test this, suppose we have two input values, a and b, and assume that f(a) = f(b).
So, let's assume that f(a) = f(b) and see if it holds true:
f(a) = (3a + 4) / 5
f(b) = (3b + 4) / 5
If we set these two equations equal to each other and solve for a and b, we can determine if they are the same or different values.
(3a + 4) / 5 = (3b + 4) / 5
Multiplying both sides of the equation by 5, we get:
3a + 4 = 3b + 4
Subtracting 4 from both sides, we have:
3a = 3b
Dividing both sides by 3, we get:
a = b
Since a and b are the same, we can conclude that the function is one-to-one.