f⁻¹(x) = ¹/₂ x - ³/₂
Further explanation
Option 1
Let
Rewrite and set the function with subject x.
Both sides are subtracted by 3.
y - 3 = 2x + 3 - 3
y - 3 = 2x
2x = y - 3
Both sides are divided by 2.
Let's replace and .
Thus, the inverse of f(x) = 2x + 3 is
Option 2
Note:
A function has an inverse if, and only if, it is one-to-one and onto.A function f is one-to-one if, for each x₁ ≠ x₂, in its domain, f(x₁) ≠ f(x₂)Let f be one-to-one and onto function with the domain A and the range B. Then its inverse function
has the domain B and the range A such that
To find the formula for the inverse of a function, solve the equation y = f(x) for x and interchange x and yLearn more The composite function Let f(x) = x + 8 and g(x) = x2 - 6x - 7. Find f(g(2)) If g(x) = (x+1)/(x-2) and h(x) = 4 – x, what is the value of g(h(-3))?
Keywords: the inverse of function, f(x) = 2x + 3, one-to-one, onto, domain, range, interchange