Subject: Mathematics
Book: Maths Mastery
An inverse function f⁻¹ swaps inputs and outputs of f: if y=f(x), then x=f⁻¹(y). Graphically, it reflects f across the line y=x. To find an inverse, replace f(x) with y, then solve for x in terms of y, and rename x as f⁻¹(y). For instance, y=2x+3 → x=(y–3)/2 → f⁻¹(x)= (x–3)/2. Inverse functions are crucial in algebraic transformations, “undoing” processes (like logs vs. exponentials), or solving equations about rates/time. Checking domain/range restrictions ensures the inverse is valid, reinforcing your function-centric problem-solving repertoire.
If a:b = 2:3 and b:c = 4:5, what is a:c?
View QuestionIf a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?
View QuestionIf a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?
View QuestionA sum of money doubles itself in 5 years at simple interest. What is the rate of interest?
View QuestionIf 2x = 16, what is the value of x?
View QuestionWhat is the value of x if 3x + 7 = 16?
View QuestionIf log(100) = 2 and log(10) = 1, what is log(1000)?
View QuestionIf a:b = 5:7 and b:c = 6:11, what is a:c?
View QuestionIf sin(A) = 1/2 and A is acute, what is the value of A?
View QuestionIf x + y = 10 and xy = 21, what is the value of x³ + y³?
View Question