what is the inverse of the function g(x)=-2/3x-5?
537942
Divide x x by 1 1 . Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=3x2+152 f - 1 ( x ) = 3 x 2 + 15 2 is the inverse of f(x)=23x−5 f ( x ) = 2 3 x - 5 .
135500
To do this, you need to show that both f(g(x)) and g(f(x)) = x. When you're asked to find an inverse of a function, you should verify on your own that the inverse you obtained was correct, time permitting. Show that f(g(x)) = x.
995054
The inverse of a function is the expression that you get when you solve for x (changing the y in the solution into x, and the isolated x into f(x), or y). Because of that, for every point [x, y] in the original function, the point [y, x] will be on the inverse.
203717
Graph an Inverse Function. Summary: After you graph a function on your TI-83/84, you can make a picture of its inverse by using the DrawInv command on the DRAW menu. For this illustration, let's use f(x) = √(x−2), shown at right.
510194
So we see that functions f and g are inverses because f ( g ( x ) ) = x f(g(x))=x f(g(x))=xf, left parenthesis, g, left parenthesis, x, right parenthesis, right parenthesis, equals, x and g ( f ( x ) ) = x g(f(x))=x g(f(x))=xg, left parenthesis, f, left parenthesis, x, right parenthesis, right parenthesis, equals, x.
459077
If g is the inverse function of f, then we often rename g as f 1. Examples. ... Therefore, g is the inverse function of f, so we can rename g as f 1, which means that f 1(x) = x 3.
329289
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=x2+3 f - 1 ( x ) = x 2 + 3 is the inverse of f(x)=2x−6 f ( x ) = 2 x - 6 .
39899
Add x x and 0 0 . Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=4x+48 f - 1 ( x ) = 4 x + 48 is the inverse of f(x)=14x−12 f ( x ) = 1 4 x - 12 .
150875
['Use the inverse function theorem to find the derivative of g(x)=3√x.', 'The function g(x)=3√x is the inverse of the function f(x)=x3. Since g′(x)=1f′(g(x)), begin by finding f′(x). Thus,', 'f′(x)=3x3.', 'f′(g(x))=3(3√x)2=3x2/3.', 'g′(x)=13x2/3=13x−2/3.']
770195
['To make the function easier to work with, first replace f(x) with y : y=2x−3.', 'To find the inverse of the relation, swap x and y : x=2y−3.', 'Solve for y : x+3=2y.']
1466723
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=3√4(−x+1)2 f - 1 ( x ) = 4 ( - x + 1 ) 3 2 is the inverse of f(x)=−2x3+1 f ( x ) = - 2 x 3 + 1 .
1402197
To find the inverse function of f(x) = x^3+2. x^3 = y-2. Taking cube root, x = (y-2) ^(1/3).
220885
['-6/2 = -3 =', '(-3)2 = 9 =', 'x2 - 6x + 9 = 9/2 + 9.']
1211269
Since g(f(x))=x g ( f ( x ) ) = x , f−1(x)=3√x+2 f - 1 ( x ) = x + 2 3 is the inverse of f(x)=x3−2 f ( x ) = x 3 - 2 .
295953
If g is the inverse function of f, then we often rename g as f 1. Examples. so g f = id. Therefore, g is the inverse function of f, so we can rename g as f 1, which means that f 1(x) = x 3.
907758
If f ( x ) = ( x − 1 ) 2 \displaystyle f\left(x\right)={\left(x - 1\right)}^{2} f(x)=(x−1)2​ on [1,∞), then the inverse function is f − 1 ( x ) = x + 1 \displaystyle {f}^{-1}\left(x\right)=\sqrt{x}+1 f−1​(x)=√​x​​​+1. The domain of f = range of f−1​ = [1,∞). The domain of f−1​ = range of f = [0,∞).
547714
y = f ̄¹(x) = 10ˣ/3 is the inverse of y = f(x) = log 3x. = x for all x in the domain of f ̄¹, and … = x for all x in the domain of f . Therefore, y = f(x) = log 3x and y = f ̄¹(x) = 10ˣ/3 are indeed inverses of each other.