This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Art, good to see you again. Here are the solutions to your problems. 1. Find the inverse function of g(x) = 3 + 4x Step 1: Replace g(x) with y. y = 3 + 4x Step 2: Swap x and y. x = 3 + 4y Step 3: Solve for y. Subtract 3 from both sides: x - 3 = 4y Divide by 4: y = (x - 3)/(4) Step 4: Replace y with g^-1(x). g^-1(x) = (x - 3)/(4) The inverse function is g^-1(x) = (x - 3)/(4). 2. Simplify 0.98 · 0.42^2 - 0.58^2 without using a calculator. Step 1: Calculate 0.42^2. 0.42^2 = 0.42 × 0.42 = 0.1764 Step 2: Calculate 0.58^2. 0.58^2 = 0.58 × 0.58 = 0.3364 Step 3: Calculate 0.98 · 0.42^2. Substitute the value from Step 1: 0.98 × 0.1764 We can write 0.98 as (1 - 0.02): (1 - 0.02) × 0.1764 = 1 × 0.1764 - 0.02 × 0.1764 = 0.1764 - 0.003528 = 0.172872 Step 4: 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 -0.163528. Send me the next one 📸