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Simplifying g(f(x)) = e2ln((4x + 5) + 3) Multiply f * x g(fx) = e2ln((4x + 5) + 3) Multiply g * fx fgx = e2ln((4x + 5) + 3) Reorder the terms: fgx = e2ln((5 + 4x) + 3) Remove parenthesis around (5 + 4x) fgx = e2ln(5 + 4x + 3) Reorder the terms: fgx = e2ln(5 + 3 + 4x) Combine like terms: 5 + 3 = 8 fgx = e2ln(8 + 4x) fgx = (8 * e2ln + 4x * e2ln) fgx = (8e2ln + 4e2lnx) Solving fgx = 8e2ln + 4e2lnx Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'gx'. f = 8e2g-1lnx-1 + 4e2g-1ln Simplifying f = 8e2g-1lnx-1 + 4e2g-1ln Reorder the terms: f = 4e2g-1ln + 8e2g-1lnx-1
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