Question

Drag the tiles to the boxes to form correct pairs.

Answer 1

Answer:

$(g + f)(2) = \sqrt 3 - 3$

$(\frac{f}{g})(-1) = 0$

$(g + f)(-1) = \sqrt{15}$

$(g * f)(2) = -3\sqrt 3$

Step-by-step explanation:

Given

$f(x) =1 - x^2$

$g(x) = \sqrt{11 - 4x$

See attachment

Solving (a): (g + f)(2)

This is calculated as:

$(g + f)(2) = g(2) + f(2)$

Calculate g(2) and f(2)

$g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}$

$f(2) = 1 - 2^2 = -3$

So:

$(g + f)(2) = g(2) + f(2)$

$(g + f)(2) = \sqrt 3 - 3$

Solving (b): $(\frac{f}{g})(-1)$

This is calculated as:

$(\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}$

Calculate f(-1) and g(-1)

$f(-1) = 1 - (-1)^2 = 0$

So:

$(\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}$

$(\frac{f}{g})(-1) = \frac{0}{g(-1)}$

$(\frac{f}{g})(-1) = 0$

Solving (c): (g - f)(-1)

This is calculated as:

$(g + f)(-1) = g(-1) - f(-1)$

Calculate g(-1) and f(-1)

$g(-1) = \sqrt{11 - 4 * -1} = \sqrt{15}$

$f(-1) = 1 - (-1)^2 = 0$

So:

$(g + f)(-1) = g(-1) - f(-1)$

$(g + f)(-1) = \sqrt{15} - 0$

$(g + f)(-1) = \sqrt{15}$

Solving (d): (g * f)(2)

This is calculated as:

$(g * f)(2) = g(2) * f(2)$

Calculate g(2) and f(2)

$g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}$

$f(2) = 1 - 2^2 = -3$

So:

$(g * f)(2) = g(2) * f(2)$

$(g * f)(2) = \sqrt 3 * -3$

$(g * f)(2) = -3\sqrt 3$