Inverse Functions notes

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inverse functions inverse functions reverse the effect of each other e.q.x 2 we can demonstrate that two functions are inverse functions by showing that: f (9 (x)) = 9(f(x)) = x this is called the identity function. example show that f(x) = 4x-1 and a(x) = 4 f (9)x)) = f (++) x++ XH = =x+1-1 9(f(x)) = g(4x-1 = (4x-1)+1 4 Since f(g(x)) = 9(f(x))=x then f(x) and g(x) are inverse functions Finding the inverse function algebraicly the inverse of f(x) is denoted as f'(x) = 4x 4 f(x) can be found algebraicaly by.. 1.0 writing f(x) as yo.... 2.0 3.0 swapping x and y 4.0 writing as p²¹(x) =.. rearranging to make x the subject letters L524 2. 4-4 =X 5 X-41 5 are inverse functions. e.q. find the inverse of f(x) = 5x +4 and state its clomain togically. (may have to factoriz if there are multiple xx's) 3₁ x - 4 = 4 S 4. f (x) = x=4 domain: x E IR e.a. find the inverse of f(x) = √3x +1 1₁ 4 =BXC+1 2. 4² ₁² = 3x+1 4²-1 = 3x 4²-1=x 3 3.x²-1 = 4₁ 3 f'(x) x+2 e.q. find the inverse of a (x) = x - 3 x+2 3₁ y = 2 + 3x Ź 14=x²-3 2. 4 (x-3) = X(+2 4x-3y=x+2 4x - x = 2 +34 x's together x (4-1) = 2 +34 x is a common factor x² = 2+34 4-1 9-¹(x) = 2 + 3x 2-1 3 e q a function only has an inverse if it is a 1-1 function (for every one input there is...

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