Find the inverse function of g(x) = 3 + 4x 2. Simplify 0.98 imes 0.422 − 0.582 without using a calculator.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to your problems.

1. Find the inverse function of $g(x) = 3 + 4x$

Replace $g(x)$ with $y$ .
$y = 3 + 4x$
Swap $x$ and $y$ .
$x = 3 + 4y$
Solve for $y$ .
Subtract 3 from both sides:
$x - 3 = 4y$
Divide by 4:
$y = \frac{x - 3}{4}$
Replace $y$ with $g^{-1}(x)$ .
$g^{-1}(x) = \frac{x - 3}{4}$
The inverse function is $\boxed{g^{-1}(x) = \frac{x - 3}{4}}$ .

2. Simplify $0.98 \cdot 0.42^2 - 0.58^2$ without using a calculator.
Calculate $0.42^2$ .
$0.42^2 = 0.42 \times 0.42 = 0.1764$
Calculate $0.58^2$ .
$0.58^2 = 0.58 \times 0.58 = 0.3364$
Calculate $0.98 \cdot 0.42^2$ .
Substitute the value from Step 1:
$0.98 \times 0.1764$
We can write 0.98 as $(1 - 0.02)$ :
$(1 - 0.02) \times 0.1764 = 1 \times 0.1764 - 0.02 \times 0.1764$ $= 0.1764 - 0.003528$ $= 0.172872$
Perform the final subtraction.
Substitute the values from Step 2 and Step 3 into the original expression:
$0.172872 - 0.3364$ $= -(0.336400 - 0.172872)$ $= -0.163528$
The simplified value is $\boxed{-0.163528}$ .

Find the inverse function of g(x) = 3 + 4x 2. Simplify 0.98 imes 0.422 - 0.582 without using a calculator.