Mathematics
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Fluidité · Pack B

Functions

Répondez à chaque question. Montrez les calculs si nécessaire.

Bronze

  1. Given $f(x) = 5x + -3$, find $f(4)$.

  2. Given $f(x) = x^2 + -4$, find $f(5)$.

  3. Given $f(x) = 4x + -1$, find $f(-2)$.

  4. Given $f(x) = 4x + -1$, find $x$ such that $f(x) = 19$.

  5. A function maps $x$ to $2x + 3$. Find the image of $7$.

  6. A function maps $x$ to $3x - 1$. What value of $x$ maps to $20$?

  7. A function $f$ has domain $\{1, 2, 3, 4, 5\}$ and rule $f(x) = 4x$. List the range.

  8. Given $g(x) = x^2 - 9$, find $g(0)$ and $g(4)$.

  9. A linear function maps $0 \to 2$ and $1 \to 6$. Find $f(x)$.

  10. A function machine multiplies by $6$ then adds $1$. Write the function $f(x)$.

Silver

  1. State the domain and range of $f(x) = 5x + -1$ where $x \in \mathbb{R}$.

  2. Find the range of $f(x) = x^2 + -2$ for $x \in \mathbb{R}$.

  3. A function $f(x) = 2x + 5$ has domain $0 \leq x \leq 6$. State the range.

  4. Given $f(x) = x + 5$ and $g(x) = 3x$, find $(f \circ g)(2)$.

  5. Given $f(x) = 3x + 2$ and $g(x) = x + 4$, find $(f \circ g)(x)$.

  6. Given $f(x) = x^2$ and $g(x) = x + 2$, find (a) $(f \circ g)(4)$ and (b) $(g \circ f)(4)$.

  7. Find the inverse of $f(x) = 5x + -4$.

  8. Given $f(x) = 3x + -2$, find $f^{-1}(13)$.

  9. A function $f$ is defined by $f: x \mapsto 3x - 9$. Find $f(4)$ and an $x$ with $f(x) = 0$.

  10. A linear function $f$ satisfies $f(1) = 7$ and $f(5) = 23$. Find $f(x)$.

Gold

  1. Given $f(x) = 2x + 5$ and $g(x) = x^2$, find $(f \circ g)(x)$.

  2. Given $f(x) = 3x + 1$ and $g(x) = x^2$, find $(g \circ f)(x)$.

  3. State the largest possible domain of $f(x) = \sqrt{x - 7}$.

  4. State the largest possible domain of $f(x) = \dfrac{1}{x - 5}$.

  5. Given $f(x) = x^2$ and $g(x) = 5x + 6$, solve $f(x) = g(x)$.

  6. Find the inverse of $f(x) = \dfrac{x + 5}{4}$.

  7. Show that for $f(x) = 2x - 5$ and $f^{-1}(x) = \dfrac{x + 5}{2}$, we have $(f \circ f^{-1})(9) = 9$.

  8. Given $f(x) = x + 5$, $g(x) = 3x$, $h(x) = x^2$, find $(f \circ g \circ h)(2)$.

  9. Given $f(x) = \sqrt{x}$ and $g(x) = x + 7$, find $(f \circ g)(18)$.

  10. Find the inverse of $f(x) = (x - 5)^2$ for $x \geq 5$.

Platinum

  1. Given $f(x) = 3x + 2$ and $g(x) = x + 5$, find $(f \circ g)^{-1}(x)$.

  2. Find the largest possible domain of $f(x) = \dfrac{1}{\sqrt{x - 6}}$.

  3. A car rental costs a £$40$ fixed fee plus £$15$ per day. (a) Write $C(n)$ for $n$ days. (b) Find $C^{-1}(c)$ and interpret.

  4. A function $f$ has graph $y = (x - 5)^2 + -3$. Find the (a) minimum value and (b) range of $f$.

  5. For $f(x) = 3x - 2$ and $g(x) = x^2 + 1$, solve $(f \circ g)(x) = 28$.

  6. A function $f(x) = ax + b$ satisfies $f(0) = 5$ and $f^{-1}(17) = 3$. Find $a$ and $b$.

  7. For $f(x) = x + 1$, find $f(f(f(x)))$.

  8. Given $f(x) = 5x + -4$, find the value of $x$ for which $f(x) = f^{-1}(x)$.

  9. A water tank has volume function $V(t) = 12t + 30$ litres after $t$ minutes ($t \geq 0$). After how many minutes does the tank contain $150$ litres?

  10. For $f(x) = \sqrt{x}$ (domain $x \geq 0$) and $g(x) = x - 7$, find the domain of $(f \circ g)(x)$.