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A function, h₁ is defined by h₁(x) = x³ + 7, where x ∈ ℝ - Scottish Highers Maths - Question 6 - 2017
Question 6
A function, h₁ is defined by h₁(x) = x³ + 7, where x ∈ ℝ. Determine an expression for h₁⁻¹ (x).
Worked Solution & Example Answer:A function, h₁ is defined by h₁(x) = x³ + 7, where x ∈ ℝ - Scottish Highers Maths - Question 6 - 2017
Step 1
Determine an expression for h₁⁻¹ (x)
Answer
To find the inverse of the function h₁(x) = x³ + 7, we start by setting y = h₁(x):
-
Set up the equation:
y = x³ + 7 -
Rearrange to find x in terms of y:
y - 7 = x³ -
Take the cube root of both sides:
x = th{3}{y - 7} -
Thus, the inverse function is defined as:
h₁⁻¹(x) = th{3}{x - 7}.