Which function is the inverse of f(x) = 2x + 3?
f-1 (x)=-1/2x-3/2
f-1 (x)=1/2x-3/2
f-1 (x)=-2x+3
f-1 (x)=2x+3

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

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