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pochemuha
3 years ago
6

1) Find the inverse function of f(x)=1/2x+3

Mathematics
2 answers:
dexar [7]3 years ago
8 0
 y = 1/2x + 3
change x and y

x = 1/2y + 3
now find the value of y and that is inverse function 

x - 3 =1/2 y
y = 2x- 6
 
f-(x) = 2x - 6
<u />

for both domain : ( - ∞ , + ∞ )

range f (x) : ( - ∞ , + ∞ )  - { 0 }
range f-(x) :( -∞ , +∞)
Gre4nikov [31]3 years ago
5 0
To find the inverse function you need to change f(x) (call it y) and x, then solve for y:

y = \frac{1}{2}x+3 \\ x = \frac{1}{2}y + 3 \\ x - 3 = \frac{1}{2}y \\ 2x-6 = y

So now you have f^{-1}(x) = 2x-6.

Composition to prove inverse relation: f \circ f^{-1} (x) = x:

f(f^{-1}(x)) = \frac{1}{2}(2x-6)+3 = x - 3 + 3 = x \square

Domain and Range of both functions is Real numbers since they are both linear equations.
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